“The sensuous may be exceedingly distinct, while intellectual concepts are extremely confused. The former we observe in the prototype of sensuous knowledge geometry; the latter, in the organon of all intellectual concepts, metaphysics. It is evident how much toil the latter is expending to dispel the fogs of confusion darkening the common intellect, though not always with the happy success of the former science.”

— Immanuel Kant

Kant's Inaugural Dissertation (1770), Section II On The Distinction Between The Sensible And The Intelligible Generally

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Immanuel Kant 200

German philosopher 1724–1804

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“The spurious axioms of the third kind from conditions proper to the subject whence they are transferred rashly to the object are plentiful, not, as in those of the Second Class, because the only way to the intellectual concept lies through the sensuous data, but because only by aid of the latter can the concept be applied to that which is given by experience, that is, can we know whether something is contained under a certain intellectual concept or not. To this class belongs the threadbare one of the schools: whatever exists contingently does at some time not exist. This spurious principle springs from the poverty of the intellect, having insight frequently into the nominal, rarely into the real, marks of contingency or necessity.”

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Kant's Inaugural Dissertation (1770), Section V On The Method Respecting The Sensuous And The Intellectual In Metaphysics

“When the interval between the intellectual classes and the practical classes is too great, the former will possess no influence, the latter will reap no benefits.”

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“The prejudices of the second species, since they impose upon the intellect by the sensual conditions restricting the mind if it wishes in certain cases to attain to what is intellectual, lurk more deeply. One of them is that which affects knowledge of quantity, the other that affecting knowledge of qualities generally. The former is: every actual multiplicity can be given numerically, and hence, every infinite quantity; the latter, whatever is impossible contradicts itself. In either of them the concept of time, it is true, does not enter into the very notion of the predicate, nor is it attributed as a qualification to the subject. But yet it serves as a means for forming an idea of the predicate, and thus, being a condition, affects the intellectual concept of the subject to the extent that the latter is only attained by its aid.”

Immanuel Kant (1724–1804) German philosopher

Kant's Inaugural Dissertation (1770), Section V On The Method Respecting The Sensuous And The Intellectual In Metaphysics

“From the imputation of confounding axioms with assumed concepts Euclid himself, however, is free. Euclid incorporated the former among his postulates while he separated the latter as common concepts—a proceeding which even on the part of his commentators was no longer understood, and likewise with modern mathematicians, unfortunately for science, has met with little imitation. As a matter of fact, the abstract methods of mathematical science know no axioms at all.”

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As quoted in "Diverse Topics: The Origin of Thought Forms," The Monist (1892) Vol. 2 https://books.google.com/books?id=8akLAAAAIAAJ&pg=PA120 ed., Paul Carus, citing The Open Court Vol. II. No. 77. A Flaw in the Foundation of Geometry by Hermann Grassmann, translated from his Ausdehnungslehre

“Formerly men had belief as to the supersensuous and thought they had knowledge of the sensuous. The science of the future, while agnostic as to the supersensuous, will replace knowledge by belief in the perceptual sphere, and reserve the term knowledge for the conceptual sphere—the region of their own concepts and ideas...”

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